# Co-ordination Number

**Description:**

Co-ordination number is the number of equidistant neighbours surrounding an atom in the given crystal structure. When the coordination number is larger, the structure is more closely packed.

1. **Simple cubic lattice **

Here any corner atom has four nearest neighbours in the same plane and two nearest neighbours in a vertical plane. Hence co-ordination number in this case is six.

2. **Body centered cubic lattice **

For any corner atom of the unit cell, the nearest atoms are the atoms which are at the centers of unit cells. A corner atom is surrounded by eight unit cells having eight body centered atoms. Hence co-ordination number is eight.

3. ** Face centered cubic lattice **

For any corner atom, there will be four face centered atoms of the surrounding unit cells in its own plane as nearest neighbours and four face centered atoms each in two perpendicular planes. Hence co-ordination number is 4 4 4 = 12.

**Number of atoms per unit cell (n):**

1. **Simple cubic lattice **

There are eight corner atoms. Each corner atom is shared by eight unit cells. Hence the share of each unit cell is equal to one eighth of an atom. Therefore the total number of atom in one unit cell = 8 x 1/8 = 1.

2. **Body centered cubic lattice**

There are eight atoms at the eight corners of the unit cell and one atom at the body centre. As each corner atom is shared by eight unit cells, the contribution to each cell is 8 x 1/8 =1. Moreover, there is one body centre atom per unit cell. Therefore total number of atoms per unit cell= 1 1 = 2.

3. **Face centered cubic lattice **

There are eight atoms at the eight corners of the unit cell and six face centered atoms at the centre of six faces. As each corner atom is shared by eight unit cells, the contribution to each cell is 8 x 1/8 =1. Each face centered atom is shared by two unit cells. Hence the contribution of six face centered atoms to each unit cell is 6 x ½ = 3. Therefore the total number of atoms per unit cell = 1 3 = 4.